The present invention relates to the transmission of binary data and is concerned particularly but not exclusively with the transmission of binary data through telephone-channels.
The practice of transmitting binary data through telephone-channels has grown substantially over the past 15 years and with developments in technology it has been possible to increase the data bit-rate (a bit is a binary digit) from about 200 bits per second (BPS) to some thousands per second despite the fact that the bandwidth of telephone-channels is only from about 500 Hz to about 3000 Hz and despite the presence of noise and other disturbances in telephone-channels which affect the signals.
The technology which has made possible this large increase in bit-rate includes within it the concept of encoding groups of bits into symbols for transmission and, at a receiver, decoding the symbols into the original groups. Hereinafter such groups are referred to as "data-words".
For example if the binary data is handled in 4-bit data-words there are 16 possible different such words ranging from 0000 to 1111 and 16 different symbols are used to represent these 16 different data-words respectively. The symbols are transmitted at a rate--known as the baud-rate--which lies within the bandwidth of the telephone-channels. With a baud-rate of 2,400 and 4-bit data-words the bit-rate is 9,600 BPS.
The symbols used to represent the data-words are waves distinguished from one another in dependence upon their phases or in dependence upon both their amplitudes and their phases.
Examples of the prior art can conveniently be described with the aid of phasor-diagrams. Examples are shown in FIGS. 1 to 4 of the accompanying drawings in which only the tips of the phasors are indicated by dots. This manner of representation has been common practice for some years--see for example IRE Transactions on Communications Systems March 1962 page 84, FIG. 4.
Referring to FIG. 1 this relates to the case in which the data is handled in 2-bit data-words. Thus four different symbols are required and these are shown at 10, 11, 12 and 13 respectively. They are equally spaced from the origin and, with reference to a phase of 0.degree. shown as the x-axis, are at phase-angles of 45.degree., 135.degree., 225.degree. and 315.degree.. The allocation of the symbols to different 2-bit data-words is a matter of choice in the encoding process.
At a co-operating receiver reference waves of 0.degree.--phase (x-axis) and 90.degree.--phase (y-axis) are generated and each received symbol is resolved into its x and y components by synchronous demodulators fed with the 0.degree. and 90.degree. reference waves respectively. A decision-making logic-network is fed with the x and y components and from these it decides which of the four symbols is received. The decision-making logic network in effect divides the signal-space shown in FIG. 1 into four decision-regions each of which is a quadrant i.e. the boundaries of the decision-regions are the intersecting x and y axes. Disturbances such as noise in the transmission channel can affect both the amplitude and the phase of a received symbol but provided a symbol is not moved out of its associated decision-region by disturbances in transmission the decision-making logic-network recovers the symbol correctly. In this way considerable tolerance to disturbances is achieved.
However, there are particular disturbances which can cause every symbol to be moved out of its related decision region in the receiver whereby gross and continuing errors occur in the decoded data.
For example, a phenomenon known as a phase-hit can occur in the transmission channel. This takes the form of large, sudden, persistent and equal changes of the phases of all symbols which can, for example, cause the y-component of each symbol to be resolved as the x-component and the negative of the x-component as the x-component at the receiver. With the receiver locked in this condition all symbols are incorrectly recovered.
To enable this problem to be substantially eliminated a technique known as differential-phase encoding was developed and has been extensively practised in systems in which the symbols are all of the same amplitude but of different phases, for example, as shown in FIG. 1. In such differential-phase encoding each data-word is not represented by a symbol per se but by a rotation or change of phase from the next-preceding symbol. At a receiver the data-words are recovered by measuring this rotation of phase and the measured rotation is decoded into the transmitted data-word. If in such a system a phase-hit should occur as previously described there are immediate errors but thereafter correct data is recovered.
FIG. 2 is a phasor-diagram applicable to the encoding of 3-bit data-words into 8 symbols. In this the symbols are again all of the same amplitude but are of 8 different phases each individual to a different one of the 8 possible different 3-bit data-words. The boundaries of the related 8 decision-regions in the decision-making logic-network at the receiver are shown in broken lines. It will be appreciated from FIG. 2 that for a given transmitted power such a system is less tolerant to disturbances of the symbols during transmission than the system described with reference to FIG. 1. Again it is usual to practise differential-phase encoding and decoding of the symbols of FIG. 2.
Referring now to FIG. 3, this relates to a technique for encoding 4-bit data-words into 16 symbols for transmission which is the subject of C.C.I.T.T. Recommendation V29.
The symbols in FIG. 3 are distinguished from one another in dependence upon both amplitude and phase and with the amplitudes and phases interrelated. Because of this, differential-phase encoding and decoding as previously described cannot be applied, However a modified form of differential encoding is employed as set out in C.C.I.T.T. Recommendation V29 which enables phase-hits to be handled in some measure.
Typical decision regions are shown by broken lines in FIG. 3 and it will be seen that for a given transmitted power there is a further reduction in the tolerance to disturbances in the transmission channel.
Users are continually seeking facilities for enabling the bit-rate to be increased and the possibility of devising apparatus for transmitting data at bit-rates of 12,000 BPS, 14,400 BPS and 16,000 BPS is currently being explored. At 12,000 BPS there are 32 symbols representing 5-bit data-words and at 14,400 BPS there are 64 symbols representing 6-bit data-words given a baud-rate of 2,400.
The performance of a transmission system using a telephone-channel is measured primarily by its tolerance to Gaussian noise in the channel. Assessments of the performance of different systems in the presence of Gaussian noise in telephone channels are to be found in the literature on the subject.
It is a general rule that for a given transmitted power the tolerance to Gaussian noise decreases sharply as the number of symbols used is multiplied. This comes about from the fact that as the number of symbols is increased they have to be more closely packed if a given transmitted power is not to be exceeded (compare FIGS. 2 and 1) and hence the decision-regions associated with the different symbols at the receiver become smaller whereby less noise-power is needed to move a symbol out of its associated decision region. It is usual to express this tolerance in terms of what is called the minimum required signal-to-noise ratio (SNR). In arriving at this minimum required SNR the minimum distance between symbols i.e., for example, the minimum distance between the dots in FIG. 3, is normalised to 2 and the minimum required SNR is given by: ##EQU1## where R.sub.1, R.sub.2 . . . R.sub.n are the amplitudes of the n symbols used. Applying this to FIG. 1 the amplitudes are equal and the normalising makes them equal to .sqroot.2. Thus the minimum SNR required is ##EQU2## For FIG. 2, the minimum SNR required=8.3 dB. For FIG. 3, the minimum SNR required=11.3 dB.
It is another general rule that for any given number of symbols and a given limit of transmitted power the tolerance to Gaussian noise improves as the symbols are spread more evenly throughout the phasor-diagram.
With this in mind it has been considered for some years that an arrangement in which all symbols are equidistant from their neighbours is superior to any other known form. In relation to a system operating at a baud-rate of 2400 and a bit-rate of 14,400 BPS the symbols for such a system would be as shown in FIG. 4--see also IEEE Transactions on Communications, Vol. COM 21, No. 10, October 1973, pages 1108 to 1115.
Although this general form has been known for some years and has been described and discussed on the assumption of a perfectly synchronised receiver it could not, in general, be put into use because no technique for enabling differential encoding and decoding to be practised with it has been devised. The invention to be described hereinafter enables this problem to be solved.